2022 · Q97
Consider the following statements :
- 1In an equilateral triangle, the centroid and centre of circumcircle coincide.
- 2Angle bisectors of a cyclic quadrilateral form another cyclic quadrilateral.
- 3Every cyclic parallelogram is a rectangle.
Which of the statements given above are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AOnly 1 and 2
- BOnly 2 and 3
- COnly 1 and 3
- D1, 2 and 3
Explanation
Statement 1: in an equilateral triangle the centroid and circumcentre coincide — true. Statement 2: the internal angle bisectors of a cyclic quadrilateral form a rectangle, which is cyclic — true. Statement 3: a cyclic parallelogram must have all angles 90°, i.e. be a rectangle — true. The keyed option is D.